Equivariant K-motives and Koszul duality

• Applicant: Dr. Jens Niklas Eberhardt
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 457441549

This project develops a novel K-theoretic approach to geometric representation theory by using methods from motivic homotopy theory. It studies torus-equivariant K-motives and defines K-theoretic versions of classical concepts such as equivariant intersection cohomology, sheaves on moment graphs and Soergel bimodules. The main goal is to prove a Koszul duality between equivariant K-motives and monodromic sheaves on flag varieties. The results work without additional gradings or mixed sheaves, which are essential in all previous approaches. This provides new perspectives on the seminal work by Beilinson–Ginzburg–Soergel on category O and Soergel's conjecture for real reductive groups.The main innovative tool is the six functor formalism for the (equivariant) stable motivic homotopy category established recently in the work of Ayoub, Cisinski–Déglise and Hoyois.

• DFG Programme: Research Grants